A Channelization Model of Landscape Evolution

Abstract

ABSTRACT. The geomorphic evolution of many landscapes is fundamentally determined by the evolution of the river channels and their interactions with hillslopes. Consequently, models of landscape evolution ought to track the evolution of the channel geometry so as to quantify the rate of erosion of channel bottoms and to follow the changes in hillslope-channel coupling over time. Unfortunately, the spatial resolution required to describe channel morphology adequately is computationally impractical. It is also beyond the resolution of most digital elevation data. What is required is a parameterization scheme for approximating fine scale channel morphology at a coarse pixel scale. Such a parameterization is already implicitly employed in most models by assuming channel equilibrium, which ties the width and depth of a model channel to the square root of discharge through a pixel. Channel fluxes are thereby predictable, and a closed form of the governing equations is attained. In reality, mountain river channels do not take a simple equilibrium form and show great spatial variability and evident disequilibrium geometry. Since the time scales of changes in channel geometry, bedrock channel erosion, and hillslope response are all closely related, it is reasonable to infer that the spatio-temporal development of the landscape is determined by their interaction and that channel disequilibrium is a fundamental factor in the dynamics of landscape evolution. If this is the case, we need an alternative sub-grid scale parameterization that aggregates channel properties such as surface morphology, roughness, cross-sectional geometry, so that the time dependent behavior of these properties can be estimated at the coarse pixel scale. We introduce such a parameterization measure, which we term channelization, after extensive investigation of the pixel resolution dependence of topographic relief. We focus in particular on the effect of coarse graining on digital elevation data for derived measures such as channel slope and upstream area and demonstrate that we can approximately correct for this effect. We show that a very simple geomorphic model can be constructed around the channelization parameter and the resolution-invariant topographic measures. This model demonstrates that channel disequilibrium may play a significant role in mountain landscape dynamics. It also shows how geomorphic models in general could be modified to incorporate such sub-pixel scale complexities and to better model these dynamics.

Tortoises and hares: dissolution, erosion and isostasy in landscape evolution

“…In contrast mechanical erosion tends to be focused on linear surface watercourses (Stark and Stark, 2001) and may be minimal on interfluves. But these contrasting processes, dissolution and erosion, are not mutually exclusive.…”

Gravel threshold of motion: a state function of sediment transport disequilibrium?

“…For example, presented a qualitative conceptual model of landscape evolution in terms of improbable system states, arguing that although deterministic process "laws" act on topography, the actual outcome (i.e., any particular landscape) depends on initial conditions and in particular is sensitive to history. Many other works have similarly generalized complex channel process and response feedbacks to understand morphodynamics (e.g., Fonstad, 2003;Phillips, 2011Phillips, , 2009Phillips, , 1991Chin and Phillips, 2007;Stark and Stark, 2001;Yanites and Tucker, 2010).…”

“…Channel morphology has long been recognized to influence sediment transport. Of particular relevance to the present work, Stark and Stark (2001) proposed a landscape evolution model with a variable called channelization that is defined as representing "the ease with which sediment can flux through a channel reach". Conceptually, channelization characterizes how changes in reach morphology influence local transport rate.…”

“…However, channelization is an abstract unitless number that does not correspond physically to any measurable aspects of morphology. A fundamental feedback is imposed in the Stark and Stark (2001) (Stark and Stark, 2001). Interestingly, the above definition of channelization could also be applied to τ * c .…”

Reconstruction of the Kinematics of Landslide and Debris Flow Through Numerical Modeling Supported by Multidisciplinary Data: The 2009 Siaolin, Taiwan Landslide

“…This disaster had a severe socio-cultural impact on Taiwanese aboriginals of the Pingpu group. Reconstruction of the burying course due to the debris avalanche event will not only bring emotional satisfaction to the surviving villagers but will provide a fundamental understanding of the complex mass movement process (Densmore et al, 1997;Densmore and Hovius, 2000;Stark and Stark, 2001;Bachmann et al, 2004;Bruckl and Parotidis, 2005;Bonnet and Crave, 2006). Contrary to the fairly precise rupturing simulation of earthquakes, the complex mass movement of landslides/debris-flows is rarely reconstructed by numerical modeling (e.g.…”